[CP2K-user] [CP2K:15238] DFT+U unphysical warning

[Krack Matthias (PSI)]

Nick, I have just committed a change to the current CP2K development (trunk) version which allows for the calculation of forces with the DFT+U method Lowdin and thus for GEO_OPT runs. The analytical stress tensor is still missing and thus CELL_OPT runs are still not possible. You may try it for your cases that did not work with Mulliken. Any feedback is welcome. We plan a CP2K 8.2 release in May which would include this change in case there are no problems.

While the computational overhead for the DFT+U method Mulliken is negligible, Lowdin requires the calculation of S**(1/2) for each new atomic configuration. The calculation of S**(1/2) requires currently a diagonalization of overlap matrix S, which can become a bottleneck for large systems. Moreover, S**(1/2) is a full matrix that does show the sparsity of S.

Matthias

> -----Ursprüngliche Nachricht-----
> Von: cp... at googlegroups.com <cp... at googlegroups.com> Im Auftrag von
> hut... at chem.uzh.ch
> Gesendet: Montag, 26. April 2021 09:42
> An: cp... at googlegroups.com
> Betreff: Re: [CP2K:15238] DFT+U unphysical warning
> 
> Hi
> 
> some information on MOLOPT basis sets and Lowdin charge derivatives:
> 
> Original MOLOPT basis sets were fully optimized for molecular energies
> under a constraint to keep a low condition number. This optimization was
> very time consuming and the resulting smallest exponents are leading to very
> expensive collocate/integrate. Joost then generated a second set
> (SR) with less primitives that keep the MOLOPT advantages but have better
> CPU performance. Later, Florian Schiffmann introduced a wavefunction
> fitting that reduced the optimization procedure.
> I have recently generated new sets based on the SR model for
> PBE/SCAN/PBE0 pseudopotentials (see https://github.com/juerghutter/BASIS
> -> MOLOPT).
> However, these are not yet tested.
> 
> Gradient for the Lowdin charges require the derivative of sqrt(S), whereas
> Mulltiken only need derivatives of S. The task is to find a way to calculate
> efficiently the derivatives of sqrt(S) as a function of the derivative of S.
> For example, this can be done for S^-1 and is widely used in QC codes.
> We have recently derived such a scheme for the gradient of the sTDA
> method.
> So now what is missing is the implementation for "plus U".
> 
> best regards
> 
> Juerg Hutter
> 
> --------------------------------------------------------------
> Juerg Hutter                         Phone : ++41 44 635 4491
> Institut für Chemie C                FAX   : ++41 44 635 6838
> Universität Zürich                   E-mail: hut... at chem.uzh.ch
> Winterthurerstrasse 190
> CH-8057 Zürich, Switzerland
> ---------------------------------------------------------------
> 
> -----cp... at googlegroups.com wrote: -----
> To: "cp2k" <cp... at googlegroups.com>
> From: "Nicholas Winner"
> Sent by: cp... at googlegroups.com
> Date: 04/26/2021 03:12AM
> Subject: Re: [CP2K:15237] DFT+U unphysical warning
> 
> 
> Matthias, that all makes a lot of sense. I think I will do a few formation
> energy comparisons at the DZV / TZV levels for my own sanity, but that's for
> me to worry about.
> 
> The one thing that remains is the issue of Lowdin vs Mulliken. I still have
> some TMOs that struggle to converge even once I switch to the SR basis sets,
> but work when using Lowdin+SR basis sets.  Of course, Lowdin does not have
> forces implemented. Do you happen to know why they have yet to be
> implemented? Based on my knowledge, Lowdin and Mulliken are just two
> different ways to get q_{mu, nu}, and so I don't see why Lowdin would not
> be implemented and Mulliken is. If it is just a matter of effort, I might fork
> Cp2k and take a look at the source, but if there is a theoretical reason for it,
> then I won't bother.
> 
> Thanks for your help,
> Nick
> On Thursday, April 22, 2021 at 1:28:41 PM UTC-7 Matthias Krack wrote:
> 
> 
>  Nick, we are talking about dense solid state systems. For such system, space
> is already well covered by a DZV basis set at each atom. The situation is,
> however, different already for  molecular liquids like water or for systems
> with larger voids (MOFs, surfaces) or even small isolated molecular systems.
> Soft functions are required to describe the electron density decaying into the
> void regions. More polarisation function (second set of  d and a set of
> functions) certainly improve the description, but  these function sets increase
> the computational costs significantly while their impact is rather moderate
> for DFT applied for O in dense solid state systems. I tried TZV/QZV and/or
> more polarisation  functions for O in such systems, but the gain was rather
> small compared to the additional computational costs. There are  tutorials
> showing how you may generate new or augment existing MOLOPT basis sets.
> It is also important to employ a balanced set of basis sets for a system which
> is, of course, also true for other system types. A mixing of SR and non-SR
> basis sets should  always be done with care. The optimisation of the SR basis
> sets includes also the condition number of the overlap matrix as a parameter
> during the basis set generation procedure which allows for a control of its
> numerical stability.
> 
>  Matthias
> 
> 
>  Von: c... at googlegroups.com <c... at googlegroups.com> Im Auftrag von
> Nicholas Winner
>  Gesendet: Donnerstag, 22. April 2021 20:34
>  An: cp2k <c... at googlegroups.com>
>  Betreff: Re: [CP2K:15205] DFT+U unphysical warning
> 
> 
>  Matthias, after investigating further, it does seem like using the SR potential
> is fairly consistent in giving good results for the DFT+U calculations, even
> when Mulliken leads to a negative +U energy. I have previously not used
> DFT+U, and always used TZV2PX  for O finding no problems, but the
> population analysis does seem to require a better conditioned overlap
> matrix.
> 
> 
> 
>  Matt mentioned TZV-SR basis sets in the UCL file, which is true, but not for
> O. In fact there are a few elements which only go up to DZVP-SR across all the
> BASIIS_MOLOPT_{, UCL, LnPP1} files. Some of these are  O, C, Cl, F, H, etc.
> which are very common elements. H for instance only has SZV-SR and the
> rest are non-SR. If I believe that SR should always be used for stability in
> condensed phase, then it seems like these need some new basis sets, at least
> up to TZV  quality. Maybe you disagree and DZVP is sufficient for these
> elements for some reason, while others really need larger bases?
> 
> 
> 
>  Is there a reference for the procedure for fitting the SR basis sets? The
> molopt sets are described in "Joost VandeVondele and Juerg Hutter, J. Chem.
> Phys. 127, 114105 (2007)", but the BASIS_MOLOPT file simply  says "variants
> of these basis sets using less and thus less diffuse primitives " were used for
> the SR versions, which is a little bit vague to me.
> 
> 
>  On Thursday, April 22, 2021 at 2:18:31 AM UTC-7 Matt W wrote:
>    Just to note there are MOLOPT-TZVP-SR in the BASIS_MOLOPT_UCL files
> distributed with CP2K.
> 
>   Matt
> 
> 
>  On Wednesday, April 21, 2021 at 11:58:19 PM UTC+1 n... at berkeley.edu
> wrote:
>    So something very strange happened.
> 
> 
> 
> 
>  I'm hesitant to switch O to a SR basis, because only SZV/DZVP are available.
> SZV isn't production quality and DZVP really isn't near the basis set limit, but I
> gave it a try to see what would happen. The warning  about negative DFT+U
> persists, but the energy changed to  -15383.653493175701442. I then re-
> initialized with TZV2PX and converged to  -15385.210534637011733.
> 
> 
> 
>  So to summarize I have three values for U=1.75
> 
>  -15378.643602015281431 with TZV2PX
> 
>  -15383.653493175701442 with DZVP
> 
>  -15385.210534637011733 after restarting TZV2PX from the DZVP wfn.
> 
> 
> 
>  These are enormous differences in energy and I don't know what to make of
> it. Any more ideas about what is going wrong based on my inputs?
> 
> 
> 
> 
>  On Wednesday, April 21, 2021 at 11:12:25 AM UTC-7 Matthias Krack wrote:
> 
> 
>   At a first glance, the basis set TZV2PX-MOLOPT-GTH-q6 for O is not well
> suited for condensed phase systems. You should rather use MOLOPT basis
> sets with “SR” in the name.
> 
>   HTH
> 
>   Matthias
> 
> 
> 
> 
> 
> 
>   Von: c... at googlegroups.com <c... at googlegroups.com> Im Auftrag von
> Nicholas Winner
>  Gesendet: Mittwoch, 21. April 2021 19:36
>  An: cp2k <c... at googlegroups.com>
>  Betreff: Re: [CP2K:15178] DFT+U unphysical warning
> 
>   Here is my input file for Mn3O4.
> 
> 
>   On Wednesday, April 21, 2021 at 10:30:13 AM UTC-7 Matthias Krack wrote:
> 
> 
>   Hello Nick
> 
>   The selection of the initial guess can help to achieve convergence. Could you
> provide a case which fails to converge with MULLIKEN? Otherwise, it is
> difficult to give further hints.
> 
>   Matthias
> 
> 
> 
> 
> 
> 
>   Von: c... at googlegroups.com <c... at googlegroups.com> Im Auftrag von
> Nicholas Winner
>  Gesendet: Mittwoch, 21. April 2021 19:15
>  An: cp2k <c... at googlegroups.com>
>  Betreff: Re: [CP2K:15176] DFT+U unphysical warning
> 
>   Thanks for the reply Matthias. I've had moderate success following what
> you suggested.
> 
> 
> 
>   One issue that still persists, however, is that for some calculations I can only
> get convergence by using PLUS_U_METHOD LOWDIN. For example, MnO
> with Ueff=1.75eV, diagonalization and small smearing (T=100). I've tried
> using diagonalization  and OT with MULLIKEN to get convergence, but
> sometimes LOWDIN seems to be the only way. Unfortunately, Lowdin does
> not support forces, so relaxations are out of the question.
> 
> 
> 
>   Do you have a suggestion for how to work around this?
> 
> 
> 
>   -Nick
> 
> 
>   On Friday, April 16, 2021 at 11:00:09 PM UTC-7 Matthias Krack wrote:
> 
> 
>   Hello Nick
> 
>   I do not recommend the use of the PLUS_U_METHOD MULLIKEN_CHARGES.
> Just use the PLUS_U_METHOD MULLIKEN. The Mulliken population analysis
> can give unphysical orbital occupations, i.e. values greater than one (UKS
> case)  or two (RKS case). Often the maximum occupation is only slightly
> exceeded and the warning can be ignored safely. You can print the orbital
> occupations for the orbitals affected by the +U correction with this  print key
> at the PRINT_LEVEL medium to check the actual occupation. Note, that the U
> values found appropriate with PW codes in the literature are not necessarily
> optimal for CP2K, too. CP2K often gives a similar effect, e.g. impact on the
> band gap, for  smaller U values.
> 
>   HTH
> 
>   Matthias
> 
> 
> 
> 
> 
> 
>   Von: c... at googlegroups.com <c... at googlegroups.com> Im Auftrag von
> Nicholas Winner
>  Gesendet: Freitag, 16. April 2021 22:57
>  An: cp2k <c... at googlegroups.com>
>  Betreff: [CP2K:15147] DFT+U unphysical warning
> 
>  Hello all, I am running some DFT+U calculations on Mn-O systems. While I
> have found a cp2k effective U value in the literature of ~1.3 eV for Mn. I
> notice that when tuning the value myself, I begin seeing the  following
> warning once the U value reaches 0.5eV.
>  *** WARNING in dft_plus_u.F:2006 :: DFT+U energy contibution is negative
> ***
>   *** possibly due to unphysical Mulliken charges!
>  Now this is only a warning, not an indication that the calculation is
> *necessarily* wrong, but it is troubling at least. Especially when my U value is
> nowhere near the size of lit value. I am using PLUS_U_METHOD
> MULLIKEN_CHARGES in order to have a marginally more robust solution.
> Does anyone have experience with how seriously to take this warning? I
> don't have a frame of reference to know if I should ignore it.
> 
>  -Nick
> 
> 
> 
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